Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 22: 18


The system of equations associated to this matrix is inconsistent - it has no solutions.

Work Step by Step

The system associated with this matrix is \begin{align*} x_1+2x_2\qquad+x_4=&3\\ x_2+3x_3\qquad=&1\\ x_3+2x_4=&0\\ 0=&2 \end{align*} Since we know that in fact $0\neq2$ we see that this system is inconsistent and cannot have any solutions.
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